基于10的幂的三种货币整数转换：加密货币无浮点数汇率计算方案

Great question—dealing with floating point precision in crypto conversions is a huge pain, so sticking to integer operations is the way to go. Let's break this down step by step using only integer arithmetic, leveraging the minimum unit definitions you provided:

Step 1: Convert Known Exchange Rates to Integer Proportions #

First, we'll translate the decimal exchange rates into integer ratios to avoid floating points entirely:

• XMR/BTC = 0.02845543: This decimal is equivalent to the fraction 2845543 / 100000000 (multiply numerator and denominator by 10^8 to eliminate the decimal).
• BTC/USD = 8435.38: This decimal is equivalent to 843538 / 100 (multiply by 10^2 to get cents, the smallest integer unit for USD).

Step 2: Map XMR to BTC's Minimum Unit (Satoshis) #

Using the XMR/BTC ratio, we can find how many satoshis equal 1 full XMR (no floating points needed):

• 1 XMR = (2845543 / 100000000) BTC
• Since 1 BTC = 10^8 satoshis, substitute that in:
  1 XMR = (2845543 / 100000000) * 10^8 satoshis
• The 10^8 terms cancel out, leaving an integer result:
  1 XMR = 2845543 satoshis

Step 3: Map Satoshis to USD's Minimum Unit (Cents) #

Next, use the BTC/USD rate to link satoshis to cents:

• 1 BTC = 843538 cents (since 8435.38 USD = 843538 cents)
• Since 1 BTC = 10^8 satoshis, this gives us:
  10^8 satoshis = 843538 cents

Step 4: Calculate XMR/USD via Integer Operations #

Now we can combine these two integer relationships to find the XMR/USD rate. To get how many cents equal 1 XMR, use cross-multiplication and integer division:

1 XMR (in cents) = (2845543 * 843538) / 100000000

If you want the XMR/USD rate in full USD (not cents), divide the result by 100 (again, integer division):

XMR/USD = (2845543 * 843538) / (100000000 * 100)

Or simplified to integer numerator and denominator:

XMR_USD_numerator = 2845543 * 843538
XMR_USD_denominator = 10000000000

Notes on Precision & Overflow #

• Integer division will truncate decimal values—if you need rounding, you can add half the denominator before dividing (e.g., (2845543 * 843538 + 50000000) / 100000000 for cent-level rounding).
• The product 2845543 * 843538 is a very large number (around 2.4e12), so make sure to use a big integer type (like Python's int or Java's BigInteger) to avoid overflow.

内容的提问来源于stack exchange，提问作者fot